Legal claims defining the scope of protection. Each claim is shown in both the original legal language and a plain English translation.
1. A method of imaging an object comprising: acquiring magnetic resonance imaging (MRI) signal data for the object using Cartesian sampling with undersampling of k-space in the phase-encoding direction at each time point of the signal dynamics, such that the undersampling pattern shifts circularly in each time frame along the phase-encoding direction and the temporal signal at spatially equidistant voxels is modulated and combined into a single aliased signal; and reconstructing an image of the object using a physical model that dictates the signal dynamics, whereby at each query voxel an equation is solved to resolve each individual temporal signal within the single aliased signal, thus yielding one or more parameters of the physical model; wherein k-space is undersampled by uniformly skipping a number of lines in the phase-encoding direction and the undersampling pattern circularly shifts in the phase-encoding direction at each subsequent time point of the signal dynamics and wherein the largest undersampling rate is restricted to the largest integer which is less than K/M; where K is the number of images and M is the number of parameters in the physical model.
This invention relates to magnetic resonance imaging (MRI) techniques for dynamic signal acquisition and reconstruction. The problem addressed is the need for efficient and accurate imaging of objects with dynamic signal behavior, such as in functional MRI or contrast-enhanced imaging, while minimizing data acquisition time and computational complexity. The method involves acquiring MRI signal data using Cartesian sampling with undersampling in the phase-encoding direction at each time point of the signal dynamics. The undersampling pattern shifts circularly along the phase-encoding direction in each time frame, causing the temporal signals from spatially equidistant voxels to modulate and combine into a single aliased signal. This approach reduces the amount of data acquired while preserving temporal information. During reconstruction, an image of the object is generated using a physical model that describes the signal dynamics. For each query voxel, an equation is solved to resolve individual temporal signals within the aliased signal, yielding one or more parameters of the physical model. The undersampling is performed by uniformly skipping lines in the phase-encoding direction, with the undersampling pattern shifting circularly at each subsequent time point. The largest undersampling rate is restricted to the largest integer less than K/M, where K is the number of images and M is the number of parameters in the physical model. This ensures sufficient data is retained for accurate reconstruction. The method enables high-speed imaging while maintaining signal fidelity and model parameter estimation.
2. The method of claim 1 , wherein the one or more parameters are selected from the group consisting of T1 relaxation rate, T2 relaxation rate, proton density, T2* relaxation rate, B0 field strength, B1 field strength, blood flow, apparent diffusion coefficient, and diffusion tensor.
This invention relates to magnetic resonance imaging (MRI) techniques for analyzing biological tissues. The method involves measuring and processing one or more parameters derived from MRI scans to assess tissue properties. The parameters include T1 relaxation rate, T2 relaxation rate, proton density, T2* relaxation rate, B0 field strength, B1 field strength, blood flow, apparent diffusion coefficient, and diffusion tensor. These parameters are used to characterize tissue composition, structure, or physiological states, enabling improved diagnostic accuracy. The method may involve acquiring MRI data, extracting the specified parameters, and analyzing them to detect abnormalities or monitor tissue changes. By leveraging multiple MRI-derived metrics, the technique provides a comprehensive assessment of tissue properties, addressing limitations of single-parameter imaging. This approach enhances the ability to differentiate between healthy and diseased tissues, improving early detection and treatment monitoring in medical applications.
3. The method of claim 1 , wherein the number of parameters per voxel is equal to the average number of k-space samples per voxel.
This invention relates to magnetic resonance imaging (MRI) and addresses the challenge of efficiently encoding and reconstructing image data from k-space samples. In MRI, k-space represents the raw data collected during scanning, and each voxel in the reconstructed image corresponds to multiple k-space samples. The invention optimizes the relationship between the number of parameters used to represent each voxel and the number of k-space samples acquired per voxel. Specifically, the method ensures that the number of parameters per voxel matches the average number of k-space samples per voxel. This balance is critical for accurate image reconstruction, as it prevents overfitting or underfitting by aligning the model complexity with the available data. The approach may involve adjusting the reconstruction algorithm or modifying the sampling strategy to maintain this equivalence. By doing so, the method improves the fidelity and efficiency of MRI image reconstruction, particularly in scenarios with limited sampling or complex imaging conditions. The invention is applicable to various MRI techniques, including accelerated imaging and compressed sensing, where precise control over data representation is essential.
4. The method of claim 1 , wherein the equation at each query voxel is solved by minimizing a least-squares cost function.
This invention relates to computational imaging techniques, specifically methods for reconstructing images from sparse or noisy data, such as in medical imaging or microscopy. The problem addressed is the challenge of accurately reconstructing high-quality images when the available data is limited or corrupted by noise, which can lead to artifacts or blurring in traditional reconstruction methods. The method involves solving an equation at each query voxel (a three-dimensional pixel) in the image to be reconstructed. The solution is obtained by minimizing a least-squares cost function, which mathematically balances the fit to the observed data while penalizing deviations from expected image properties. This approach improves reconstruction accuracy by systematically reducing errors in the presence of noise or missing data. The least-squares optimization ensures that the reconstructed image adheres closely to the measured data while maintaining smoothness or other desired characteristics, depending on the specific constraints applied. This technique is particularly useful in applications where data acquisition is expensive or time-consuming, such as in magnetic resonance imaging (MRI) or electron microscopy, where reducing scan time or radiation exposure is critical. The method can be applied to various imaging modalities and data types, providing a robust framework for high-quality image reconstruction under challenging conditions.
5. The method of claim 4 , wherein the least-squares cost function is: I n ( m , t l ) - ∑ r = 1 - ⌈ R 2 ⌉ ⌊ R 2 ⌋ w r ( t l ) s n - r N R ( m ) f ( x → n - r N R , t l ) 2 wherein: I n (m,t l ) is the aliased signal at voxel n, coil index m, and the time point t l ; w r (⋅) is the modulation function for the aliasing signal at voxel n - r N R ; s n - r N R ( m ) is the coil sensitivity of the mth coil at the aliasing voxel n - r N R ; f(⋅,t l ) is the underlying signal model; x → n - r N R is the unknown parameter at the aliasing voxel n - r N R ; R is the acceleration factor; N is the total number of lines in the phase-encoding direction; and the symbols └⋅┘ and ┌⋅┐ represent the largest integer less than and the smallest integer greater than the argument, respectively.
This invention relates to magnetic resonance imaging (MRI) reconstruction techniques, specifically addressing the problem of aliasing artifacts in accelerated imaging. The method involves a least-squares cost function designed to reconstruct an unaliased image from undersampled k-space data. The cost function minimizes the difference between the measured aliased signal and a model that accounts for multiple aliased contributions. The aliased signal at a given voxel, coil, and time point is compared to a weighted sum of underlying signals from aliased voxels, where each contribution is modulated by coil sensitivity and an underlying signal model. The modulation function adjusts for the aliasing effect, while the signal model incorporates unknown parameters at the aliased voxels. The acceleration factor and total phase-encoding lines determine the range of aliased voxels considered. Floor and ceiling functions ensure proper indexing of aliased contributions. This approach enables accurate reconstruction of unaliased images from undersampled data, improving imaging speed and quality in MRI.
6. The method of claim 5 , wherein the f(⋅,t l ) and x → n - r N R terms are substituted for a specific physical model.
This invention relates to a method for improving the accuracy of a physical model by substituting specific terms in the model with alternative mathematical expressions. The method addresses the challenge of refining predictive models in scientific and engineering applications where traditional formulations may lack precision or fail to capture certain physical phenomena accurately. The substitution involves replacing the terms f(⋅,t l) and x → n - r N R in the model with a specific physical model that better represents the underlying system. The term f(⋅,t l) typically represents a function dependent on time and other variables, while x → n - r N R may denote a spatial or state transition component. By incorporating a more accurate physical model, the method enhances the model's predictive capabilities, reducing errors in simulations or real-world applications. This approach is particularly useful in fields such as fluid dynamics, structural mechanics, or electromagnetics, where precise modeling is critical. The substitution ensures that the model aligns more closely with observed physical behavior, leading to improved reliability and performance in engineering and scientific analyses.
7. The method of claim 6 , wherein the f(⋅,t l ) and x → n - r N R terms are replaced f ( · , t l ) = A - B exp ( - t l T 1 ) and x → n - r N R = [ A n - r N R , B n - r N R , T 1 n - r N R ] T where [ . . . ] T represents the vector transpose.
This invention relates to mathematical modeling and optimization techniques, specifically for improving the accuracy and efficiency of parameter estimation in dynamic systems. The problem addressed involves refining the functional form of a time-dependent parameter f(⋅,t l) and its associated vector x → n - r N R to enhance computational performance and model precision. The original method uses a general functional form for f(⋅,t l) and a vector x → n - r N R to represent system parameters. The improvement replaces these with a specific exponential decay model, where f(⋅,t l) is defined as A - B exp(-t l T 1), and x → n - r N R is structured as a column vector [A n - r N R, B n - r N R, T 1 n - r N R] T, with T denoting the vector transpose. This modification simplifies the parameter estimation process by reducing the complexity of the mathematical expressions while maintaining or improving model accuracy. The exponential decay form is particularly useful for systems where parameters exhibit time-dependent behavior that can be approximated by such a model. The vector representation ensures that the parameters A, B, and T 1 are systematically organized, facilitating easier integration into optimization algorithms and computational frameworks. This approach is applicable in fields such as control systems, signal processing, and data analysis, where precise parameter estimation is critical for system performance.
8. The method of claim 6 , wherein the f(⋅,t l ) and x → n - r N R terms are replaced by f ( · , t l ) = A exp ( - t l T 1 ) and x → n - r N R = [ A n - r N R , T 2 n - r N R ] T .
This invention relates to signal processing techniques for improving the accuracy of time-of-flight (ToF) measurements in systems such as radar, lidar, or ultrasonic sensors. The problem addressed is the need for more precise distance and velocity estimation in noisy or dynamic environments where traditional methods suffer from errors due to signal distortion or multipath interference. The method involves modifying key mathematical terms in a signal model to enhance estimation performance. Specifically, the terms f(⋅,t l) and x → n - r N R are replaced with f(⋅,t l) = A exp(-t l T 1) and x → n - r N R = [A n - r N R, T 2 n - r N R] T. The first term, f(⋅,t l), represents a time-dependent signal component modeled as an exponential decay with amplitude A and decay rate T 1, which improves tracking of signal attenuation over time. The second term, x → n - r N R, defines a state vector for a target's position and velocity, where A n - r N R is the amplitude of the reflected signal and T 2 n - r N R is the time delay, enabling more accurate state estimation. This approach refines the signal model to better account for real-world signal behavior, reducing estimation errors and improving robustness in applications requiring high-precision distance and velocity measurements.
9. The method of claim 5 , wherein the least-squares cost function is minimized by an unconstrained optimization algorithm or a dictionary-based exhaustive search algorithm.
This invention relates to optimization techniques for minimizing a least-squares cost function in signal processing or data analysis applications. The problem addressed involves efficiently solving optimization problems where the goal is to minimize a least-squares cost function, which is a common objective in regression analysis, machine learning, and other computational tasks. Traditional optimization methods may be computationally expensive or impractical for large-scale problems, leading to the need for more efficient algorithms. The invention describes a method for minimizing a least-squares cost function using either an unconstrained optimization algorithm or a dictionary-based exhaustive search algorithm. The unconstrained optimization algorithm operates without constraints, allowing for flexible and adaptive minimization of the cost function. Alternatively, the dictionary-based exhaustive search algorithm systematically evaluates possible solutions from a predefined set of candidates, ensuring that the optimal solution is found through exhaustive comparison. This approach improves computational efficiency and accuracy in scenarios where traditional methods may fail or perform suboptimally. The method is particularly useful in applications requiring real-time processing or handling large datasets, where speed and precision are critical.
10. The method of claim 9 , wherein the minimization of the least-squares cost function is solved using an algorithm selected from the group consisting of steepest descend, conjugate gradients, Gauss-Newton and Levenberg-Marquardt.
This invention relates to optimization techniques for minimizing a least-squares cost function in computational systems, particularly in applications requiring efficient parameter estimation or model fitting. The problem addressed is the computational inefficiency and potential instability of traditional optimization methods when applied to complex, high-dimensional least-squares problems. The invention provides a method for solving such problems using one of several well-known optimization algorithms: steepest descent, conjugate gradients, Gauss-Newton, or Levenberg-Marquardt. Each algorithm is selected based on the specific requirements of the problem, such as convergence speed, numerical stability, or computational resource constraints. Steepest descent is a simple gradient-based method suitable for smooth cost functions, while conjugate gradients improve convergence by incorporating information from previous iterations. Gauss-Newton and Levenberg-Marquardt are iterative methods that approximate the Hessian matrix, making them particularly effective for nonlinear least-squares problems. The method ensures robust and efficient minimization by leveraging the strengths of these algorithms, depending on the problem's characteristics. This approach is applicable in fields such as machine learning, signal processing, and control systems, where accurate and efficient parameter estimation is critical.
11. The method of claim 10 , wherein the minimization of the least-squares cost function is solved using an algorithm selected from the group consisting of Gauss-Newton and Levenberg-Marquardt.
This invention relates to optimization techniques for minimizing least-squares cost functions in computational systems, particularly in applications requiring iterative numerical optimization. The problem addressed is the efficient and accurate minimization of such functions, which are commonly encountered in parameter estimation, curve fitting, and machine learning tasks. Traditional optimization methods may suffer from slow convergence, numerical instability, or suboptimal solutions, particularly in high-dimensional or non-linear scenarios. The method involves solving the minimization problem using iterative optimization algorithms specifically designed for least-squares cost functions. The optimization process leverages either the Gauss-Newton or Levenberg-Marquardt algorithm. The Gauss-Newton method approximates the Hessian matrix using the Jacobian, making it computationally efficient for non-linear least-squares problems. The Levenberg-Marquardt algorithm combines the advantages of gradient descent and Gauss-Newton by incorporating a damping parameter to improve stability and convergence, especially in ill-conditioned problems. Both methods are well-suited for scenarios where the objective is to minimize the sum of squared residuals between observed and predicted values, such as in regression analysis or model fitting. The approach ensures robust convergence by adaptively adjusting parameters during iteration, reducing the risk of divergence or local minima. This method is particularly useful in applications requiring high precision, such as scientific computing, signal processing, and automated control systems. The selection of either algorithm depends on the specific characteristics of the problem, with Levenberg-Marquardt often preferred for its balance betwe
12. The method of claim 1 , wherein the imaging method is a medical imaging method.
This invention relates to medical imaging techniques, specifically addressing the need for improved imaging methods to enhance diagnostic accuracy and patient outcomes. The method involves capturing medical images using imaging modalities such as X-ray, MRI, CT, or ultrasound. The imaging process includes acquiring raw image data, processing the data to reduce noise and artifacts, and generating a final high-quality medical image suitable for clinical analysis. The method may incorporate advanced algorithms for image enhancement, such as noise reduction, contrast adjustment, and artifact correction, to improve image clarity and diagnostic reliability. Additionally, the method may include automated segmentation or annotation features to highlight specific anatomical structures or abnormalities, aiding radiologists and clinicians in interpretation. The technique ensures that the imaging process is optimized for speed, accuracy, and patient safety, reducing the need for repeat scans and minimizing radiation exposure where applicable. The invention is particularly useful in diagnostic imaging, where precise and clear images are critical for accurate diagnosis and treatment planning.
13. The method of claim 12 , wherein the medical imaging method is magnetic resonance imaging (MRI).
This invention relates to medical imaging techniques, specifically addressing the challenge of improving image quality and diagnostic accuracy in medical imaging systems. The method involves processing medical imaging data to enhance image clarity and reduce artifacts, particularly in magnetic resonance imaging (MRI). The technique includes acquiring raw imaging data from a medical imaging device, such as an MRI scanner, and applying a series of computational steps to refine the data. These steps may include noise reduction, artifact correction, and signal enhancement to produce a final high-quality image. The method may also involve adjusting imaging parameters based on patient-specific factors to optimize image quality. Additionally, the technique may incorporate machine learning algorithms to predict and correct imaging distortions in real-time. The goal is to provide clearer, more accurate medical images that improve diagnostic reliability and patient outcomes. The method is particularly useful in MRI, where image clarity is critical for detecting and diagnosing medical conditions.
14. The method of claim 12 , wherein the medical imaging method is adapted and configured to image one or more organs selected from the group consisting of the heart, liver, kidneys, abdomen, breast, prostate, brain, knee, and any muscularskeletal system.
This invention relates to a medical imaging method designed to capture detailed images of specific organs and anatomical structures. The method is configured to image one or more organs, including the heart, liver, kidneys, abdomen, breast, prostate, brain, knee, and components of the musculoskeletal system. The imaging technique is adapted to provide high-resolution visualizations of these organs, enabling accurate diagnosis and assessment of medical conditions. The method may involve advanced imaging modalities such as MRI, CT, ultrasound, or other techniques tailored to the specific anatomical region being examined. By focusing on these key organs and systems, the method supports early detection of diseases, monitoring of treatment progress, and precise surgical planning. The adaptability of the imaging method ensures compatibility with various medical imaging devices and protocols, enhancing its versatility in clinical and research settings. The invention addresses the need for reliable, high-quality imaging solutions that can be customized for different anatomical targets, improving diagnostic accuracy and patient care.
15. The method of claim 12 , wherein the medical imaging method is at least one selected from the group consisting of cardiac tissue characterization, detection of edema, detection of iron overload in the heart and liver, water-fat separation imaging, clinical neuralimaging, functional MRI, tumor imaging, flow mapping, mapping of apparent diffusion coefficient, diffusion tensor imaging, and magnetic resonance fingerprinting.
This invention relates to medical imaging techniques for analyzing biological tissues and structures. The method involves using magnetic resonance imaging (MRI) to assess various physiological and pathological conditions by characterizing tissue properties. The technique can be applied to cardiac tissue characterization, detecting edema, identifying iron overload in the heart and liver, water-fat separation imaging, clinical neural imaging, functional MRI, tumor imaging, flow mapping, mapping of the apparent diffusion coefficient (ADC), diffusion tensor imaging (DTI), and magnetic resonance fingerprinting. Each application leverages specific MRI sequences and processing algorithms to extract quantitative or qualitative information about tissue composition, structure, or function. For example, cardiac tissue characterization may involve T1 or T2 mapping to assess myocardial health, while edema detection relies on signal intensity changes in fluid-filled regions. Iron overload detection uses susceptibility-weighted imaging or T2* mapping to quantify iron deposition. Water-fat separation imaging differentiates fat and water signals for metabolic or structural analysis. Clinical neural imaging may include diffusion-based techniques to study brain connectivity or functional MRI to assess brain activity. Tumor imaging can involve contrast-enhanced or diffusion-weighted MRI to evaluate tumor properties. Flow mapping measures blood flow dynamics, while ADC and DTI provide insights into tissue microstructure. Magnetic resonance fingerprinting enables simultaneous multi-parameter quantification. The method improves diagnostic accuracy by providing detailed, non-invasive assessments of tissue properties for various medical conditions.
16. The method of claim 1 , further comprising one or more additional imaging acceleration methods selected from the group consisting of SENSE (parallel imaging), partial Fourier techniques, and simultaneous multi-slice techniques.
This invention relates to magnetic resonance imaging (MRI) techniques, specifically methods for accelerating image acquisition to reduce scan time. The primary challenge addressed is the inherently slow data collection process in MRI, which can lead to long scan times and patient discomfort. The invention enhances MRI speed by incorporating additional imaging acceleration methods alongside a base technique. These methods include SENSE (Sensitivity Encoding for Fast MRI), which uses multiple receiver coils to reduce scan time by acquiring data in parallel; partial Fourier techniques, which reconstruct images from incomplete k-space data to shorten acquisition; and simultaneous multi-slice techniques, which capture multiple image slices at once. By combining these acceleration methods, the invention improves MRI efficiency without compromising image quality, making the technology particularly useful in clinical settings where rapid imaging is critical. The approach leverages existing MRI hardware and software capabilities to optimize data acquisition, reducing patient scan times and improving workflow in diagnostic imaging.
17. The method of claim 1 , wherein the noise amplification due to the acceleration is quantified by the dynamics-factor (d-factor) in the absence of parallel imaging, or the dynamics-geometry-factor (dg-factor) in the presence of parallel imaging.
This invention relates to magnetic resonance imaging (MRI) techniques, specifically addressing the problem of noise amplification in dynamic imaging sequences. The method quantifies noise amplification caused by acceleration in MRI scans, which is a critical issue in fast imaging protocols. The quantification is performed using a dynamics-factor (d-factor) when parallel imaging is not employed, or a dynamics-geometry-factor (dg-factor) when parallel imaging is used. These factors account for the trade-offs between scan speed and image quality, allowing for optimized imaging parameters. The d-factor and dg-factor provide a standardized metric to assess how acceleration affects signal-to-noise ratio (SNR) in dynamic MRI sequences, enabling clinicians and engineers to balance imaging speed with image fidelity. The method ensures that noise amplification is accurately measured and mitigated, improving diagnostic accuracy in time-sensitive applications such as cardiac or functional MRI. By incorporating these factors, the technique enhances the reliability of accelerated MRI protocols, making them more suitable for clinical and research use.
18. The method of claim 1 , wherein the method is adapted and configured for 2D parametric mapping applications.
This invention relates to a method for 2D parametric mapping applications, which involves analyzing and visualizing spatial variations of a parameter across a two-dimensional region. The method addresses the challenge of accurately mapping and quantifying parameters such as tissue properties, material characteristics, or other spatially varying quantities in medical imaging, materials science, or engineering. The method includes acquiring data from a region of interest, processing the data to extract parametric information, and generating a 2D map that represents the spatial distribution of the parameter. The processing step may involve mathematical modeling, signal processing techniques, or machine learning algorithms to derive the parameter values. The resulting 2D map provides a visual representation of how the parameter varies across the region, enabling detailed analysis and interpretation. The method is particularly useful in applications where understanding spatial variations is critical, such as medical imaging for diagnosing tissue abnormalities, materials science for characterizing material properties, or engineering for assessing structural integrity. By providing a clear and accurate 2D parametric map, the method enhances decision-making in these fields. The technique ensures high precision and reliability, making it suitable for both research and clinical applications.
19. The method of claim 1 , wherein the method is adapted and configured for 3D parametric mapping applications.
This invention relates to a method for 3D parametric mapping applications, addressing the need for precise and efficient spatial data analysis in three-dimensional environments. The method involves capturing and processing data from a physical space to generate a parametric model that accurately represents the spatial relationships and characteristics of objects within that space. The parametric model is used to derive quantitative measurements, such as distances, volumes, and surface areas, with high accuracy. The method includes steps for data acquisition, preprocessing, and parametric modeling, ensuring that the resulting model can be dynamically adjusted based on input parameters. This adaptability allows for real-time adjustments and improvements in mapping accuracy. The method is particularly useful in applications requiring detailed 3D spatial analysis, such as architectural design, medical imaging, and industrial inspection, where precise measurements and dynamic modeling are critical. The invention enhances the efficiency and reliability of 3D parametric mapping by integrating advanced data processing techniques to minimize errors and improve computational performance.
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February 4, 2020
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